Thank you for the good question. Did not realize there were options on the mini splits. My wife likes things not conspicuous, so may look into hidden units. Do you think the commercial line will be the way to go for a bigger house?
Don't know much about geothermal. I'll ask our building science mechanical consultant.
The commercial line of Mitsubishi is certainly a great fit for a 7k sqft home. The big thing For you would be fewer outside units (possibly only one or two) and the ability to heat and cool at the same time. Only problem you might run into is finding someone who will install them.
Geothermal is amazing when installed correctly. We work on several but generally refuse to install them. if we were a larger company we would be more willing to put them in but we have to rely on a contractor to dig our lines and it prices us out of the market. Big downfall of geothermal is the obvious cost on Installation and repair. Otherwise they generally last forever when installed correctly.
if you have any specific HVAC questions send me a pm with your number and I’ll call you. I can also give you some advice on questions to ask you HVAC contractor and designer.